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The point you make about it being usually implausible that a scientist
will treat a pet theory as falsified because of apparently contrary
evidence is well understood and accepted among Popperian philosophers
of science. The man who has discussed this in the most sophisticated
way was Imre Lakatos, who argued that what we ought to assess are not
individual theories taken in isolation, almost all of which will seem
incompatible with some datum here or there, but "problemshifts" --
sequences of successively modified theories, which may react to data
in ways that progressively enrich their testable consequences, or may
react by increasingly sealing themselves off from any logical
possibility of refutation.
Your rhetorical questin "What could falsify the statement 'Scientific
theories should be falsifiable'?" would not be accepted by Popperians
as a reasonable criticism, because Popper's demarcation criterion was
very explicitly put forward as demarcating empirical science from
other forms of discourse; it was never claimed to demarcate sense from
nonsense more generally, and certainly does not. "Scientific theories
should be falsifiable" is not, and is not intended to be, an assertion
of empirical science; nor is, for instance, "It is wrong to kill
people".
Cllr Prof. G.R. Sampson MA PhD MBCS
Professor of Natural Language Computing
School of Cognitive & Computing Sciences
University of Sussex
Falmer, Brighton BN1 9QH, GB
e-mail geoffscogs.susx.ac.uk
tel. +44 1273 678525
fax +44 1273 671320
web http://www.grsampson.net

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With regards to whether statements should be falsifiable or useful
four points, I think, should be considered:
1. Much of the rhetoric and the models of the �Eurooetheory of
science�Euro have developed out of the natural sciences which are
characterized by the unrestricted validity of one paradigm only. In
contrast to the natural sciences, linguistics has never experienced
the existence of such a strong paradigm. Thus, statements such as the
following are of little relevance to the daily research of many
(probably most) linguists.
(1) Sentences of natural language never surpass 1,173 letters in length.
(2) Agents, more often than not, but not always, are expressed as
topics. Such statements (=hammer) are therefore not falsified if they
fail to tune anyone's guitar (= research) but are merely of no
practical consequence whatsoever.
2. I think that there is a general agreement in philosophy that Karl
Popper thought to well of scholars and their work. Few scholars
(probably no one) would make a theoretical statement in order that
it'll be falsified. Rather, they will throw their whole energy
on the task to seek evidence for their claim and thereby expand the
theoretical statement. They are more likely to produce useful
statements than falsifiable ones.
3. Neither falsifiability nor usefulness seems to be the most
important attribute of a theoretical statement but its capability to
open the way for new research, that is, to create work. A theoretical
statement thus usually provides for what T.S. Kuhn has termed
"normal science".
4. Theoretical statements, generally, are more likely to be falsified
(or clarified) than not. However, history of linguistics is full of
examples that falsification evolves rather slowly; certainly, much
slower than Popper tried to make us believe. Nevertheless, I would
argue that falsification does account for theory shifts (and follow
Popper up to this point). Such shifts are, however, slowed down by the
practice of "normal science". Can falsifiable statements be
falsified more quickly? Certainly yes. But does this make them more
useful?
Patrick Heinrich